1) No, the new PSP is not even released yet and you can be quite sure all currently known exploits will be patched on it (as they are with the latest original psp's firmware). All you can do is wait and see if/when the new models are hacked.
2) Current PSPs can be downgraded to allow homebrew to run if they are running firmware 3.30 or below. There is no way to run homebrew on a PSP that has been updated to 3.31 as of yet.
Depending on what firmware the PSP is running, you may or may not need a copy of a certain game to downgrade (either an original copy of GTA: Liberty City Stories with firmware 2.0 on the UMD or an original release of lumines).
This is because the only way found to get around sony's new security measures is through exploits found in those particular games.
3)Yes, once you have downgraded/updated to a custom firmware its all done (a custom firmware is an unofficial hacked firmware that allows homebrew to run like on a firmware 1.5 PSP, but also run the latest UMD games). The only issue is running games released in the future that will need a higher firmware to run. You have to hope there will continue to be new versions of the custom firmwares made.
4) You can install HEN (Homebrew ENabler) and the eloader on certain firmwares and run homebrew with that. It really makes more sense to downgrade to 1.5 if you are able to in my opinion. To run HEN requires the same access as a downgrader (Ie if you need a certain game UMD to downgrade, you need it to unstall HEN also).
If you want to play a PSP game on your PSP then you just buy the UMD, you will not receive any help on pirating them on this site.
5)Downgrading to 1.5 gives you homebrew access but you dont get any of the features of newer firmwares like the web browser and you cannot run newer PSP games as they require more recent firmwares.
You can use an application called devhook to load (untill you power down the PSP) a more recent firmware from the memory stick instead of installing it and loosing homebrew.
There is also the custom firmwares I described above.
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